A message in the Morse code is a finite sequence(a word) with dots, dashes and gaps. How many different messages can be made with $7$ dots,$3$ dashes and $2$ gaps? And how many if it is not allowed that the message begins and ends with a gap?
I think that there are $7! \cdot 3! \cdot 2!$ different messages, that can be made with $7$ dots,$3$ dashes and $2$ gaps. Is this correct?